The Complexity of Quickly ORM-Decidable Sets

  • Joel D. Hamkins
  • David Linetsky
  • Russell Miller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4497)


The Ordinal Register Machine (ORM) is one of several different machine models for infinitary computability. We classify, by complexity, the sets that can be decided quickly by ORMs. In particular, we show that the arithmetical sets are exactly those sets that can be decided by ORMs in times uniformly less than \({\ensuremath{\omega^\omega}}\). Further, we show that the hyperarithmetical sets are exactly those sets that can be decided by an ORM in time uniformly less than \(\omega_1^{CK}\).


Ordinal ordinal computation infinite time computation computability register machine arithmetical hierarchy hyperarithmetical hierarchy complexity 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Joel D. Hamkins
    • 1
  • David Linetsky
    • 2
  • Russell Miller
    • 3
  1. 1.The College of Staten Island of CUNY and The CUNY Graduate CenterUSA
  2. 2.The CUNY Graduate Center, 365 Fifth Avenue, New York NY 10016USA
  3. 3.Queens College of CUNY and The CUNY Graduate CenterUSA

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